As far as I'm aware, using plr:GetMouse() to get the player's mouse has limitations and unfortunately, being able to check if the key is held down is one of those limitations.
One thing you can do is use the mouse.KeyDown event connected to a function that starts sprinting, then use mouse.KeyUp to stop sprinting. This is the faster way of answering your question. (But honestly, these are deprecated and you should totally be using UserInputService)
To do this with UserInputService, it would be something like:
game:GetService("UserInputService").InputBegan:Connect(function(input, gameProcessed)
end)
game:GetService("UserInputService").InputEnded:Connect(function(input, gameProcessed)
end)
Relevant links that I think might help in some way:
UserInputService.InputBegan
UserInputService.InputEnded
UserInputService.IsKeyDown
Enum.KeyCode